Probability and Statistics I is the foundation upon which all data science, actuarial modeling, and modern research are built. It is the mathematical language of uncertainty. Whether you are calculating the likelihood of a specific event or trying to make sense of a massive dataset, these concepts are your primary tools. For students, this unit is often the first major hurdle in quantitative studies, requiring a shift from “plug-and-play” math to logical reasoning.
Below is the exam paper download link
PDF Past Paper On Probability And Statistics I For Revision
Above is the exam paper download link
To sharpen your skills for the upcoming exam, we have put together a focused Q&A revision guide covering the core pillars of the syllabus.
What is the difference between Mutually Exclusive and Independent Events?
This is a classic exam trap. Mutually Exclusive events are those that cannot happen at the same time—like flipping a coin and getting both a Head and a Tail. If one happens, the probability of the other becomes zero. Independent Events, however, are those where the outcome of one does not affect the other. For example, rolling a 6 on a die and then flipping a Head on a coin are independent; the die doesn’t “care” what the coin did.
How do we apply the Multiplication Rule?
The Multiplication Rule is used to find the probability of two events occurring together.
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For independent events: $P(A \text{ and } B) = P(A) \times P(B)$.
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For dependent events (where $A$ affects $B$): $P(A \text{ and } B) = P(A) \times P(B|A)$.
Understanding this distinction is vital when solving “sampling without replacement” problems, which are a staple of Probability and Statistics I past papers.
What are ‘Discrete’ vs ‘Continuous’ Random Variables?
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Discrete Variables: These are countable values, like the number of students in a lecture hall or the number of defective bulbs in a box. We often use the Binomial or Poisson distributions to model these.
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Continuous Variables: These can take any value within a range, such as height, weight, or time. These are modeled using the Normal Distribution (the famous Bell Curve).
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Why is the ‘Mean’ sometimes misleading?
In statistics, the mean (average) is sensitive to outliers—extremely high or low values that don’t represent the rest of the data. For instance, if nine people earn Kshs 20,000 and one person earns Kshs 1,000,000, the “average” income will look very high, even though 90% of the group is struggling. This is why examiners often ask you to compare the Mean with the Median or Mode to get a clearer picture of data distribution.
What does the ‘Standard Deviation’ actually tell us?
The Standard Deviation is a measure of “spread.” A low standard deviation means the data points are clustered closely around the mean, suggesting consistency. A high standard deviation means the data is spread out, indicating high variability. In an exam, you might be asked to use this to compare the “risk” or “reliability” of two different datasets.
What is the ‘Law of Large Numbers’?
This principle states that as you perform an experiment more times (increasing your sample size), the actual results will get closer and closer to the expected theoretical probability. This is why casinos always win in the long run—even if one player wins big, the thousands of other plays ensure the “house edge” remains intact.
Conclusion
Success in Probability and Statistics I comes down to identifying which “tool” to use for which “problem.” Do you need a Permutation or a Combination? Is this a Normal or a Binomial distribution? The only way to build this intuition is through consistent practice with actual exam questions.
To help you get started, we have provided a link to a comprehensive revision resource below. Download it, time yourself, and master the logic of uncertainty.
Last updated on: March 24, 2026